A highway project requires excavation over a $100\text{-meter}$ section. The cross-sectional areas of the cut at the beginning (Station $0+000$) and the end (Station $0+100$) are $A_1 = 40 \text{ m}^2$ and $A_2 = 60 \text{ m}^2$, respectively. A survey taken exactly at the midpoint (Station $0+050$) reveals the cross-sectional area there is $A_m = 52 \text{ m}^2$. Calculate the volume of earthwork using the highly accurate Prismoidal Formula.

A mass haul diagram analysis yields a balance line. Above this balance line is a massive cut/fill loop representing $10,000 \text{ cubic meters}$ of total earthwork. The Free Haul Distance (FHD) specified in the contract is $500 \text{ meters}$. A horizontal line of length $500 \text{ m}$ is drawn inside the loop, intersecting the curve at two points. The volume ordinate at this horizontal $500\text{ m}$ line is $7,000 \text{ m}^3$.

A crushed stone base course has a laboratory maximum dry density (MDD) of $2,150 \text{ kg/m}^3$ as determined by the Modified Proctor Test. A field sand-cone test is performed on the compacted base layer. The field test determines the bulk (wet) density of the soil in place is $2,280 \text{ kg/m}^3$ and the field moisture content is $8.5\%$. The project specification requires a minimum relative compaction of $98\%$. Does this section pass the compaction test?

An engineer inspects a five-year-old asphalt highway. In the right lane (heavy truck lane), there are deep, continuous longitudinal depressions right where the wheel paths are located. In the left lane (passenger car lane), there is a network of interconnected cracks resembling the skin of an alligator. Identify these two specific types of distresses and explain their primary mechanical causes.

A contractor has won a bid to construct a $10\text{-kilometer}$ rural highway. The project involves:

Recommend the primary piece of heavy equipment best suited for each of these three specific tasks.